Geometric Proof Practice Questions

Work out angle $ABC$.

Give a reason for your answer.

Work out angle $OAC$.

Give a reason for your answer.

Write down the size of angle $DBC$.

Give a reason for your answer.

Work out angle $ADC$.

Give reasons for your answer.

Work out angle $TAB$.

Give reasons for your answer.

Hence write down the size of angle $ACB$.

Give a reason for your answer.

Show that each interior angle of the pentagon is $108°$.

Prove that angle $BXC = 108°$.

Give reasons for your working.

Explain why angle $ABC$ + angle $BCD = 180°$.

Prove that angle $ADC$ = angle $BCD$.

$AB$ is a diameter of a circle, centre $O$.

$C$ is a point on the circle.

The tangent to the circle at $C$ meets $AB$ extended at $T$.

Angle $CAB = x$ and angle $CTB = y$.

Not drawn accurately

Prove that $y = 90 - 2x$

$AB$ is a chord of a circle, centre $O$.

$M$ is the midpoint of $AB$.

Not drawn accurately

Using congruent triangles, prove that $OM$ is perpendicular to $AB$.

$A$, $B$ and $C$ are points on a circle.

$SAT$ is the tangent to the circle at $A$.

$SAT$ is parallel to $BC$.

Not drawn accurately

Prove that $AB = AC$.

Give reasons for each step of your proof.